The grades on a language midterm at Loyola are normally distributed with $\mu = 69$ and $\sigma = 5.0$. Omar earned a n $84$ on the exam. Find the z-score for Omar's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Omar's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{84 - {69}}{{5.0}}} $ ${ z \approx 3.00}$ The z-score is $3.00$. In other words, Omar's score was $3.00$ standard deviations above the mean.